The last semicolon is the key here. When Vim tries to locate the 'tags' file, it first looks at the current directory, then the parent directory, then the parent of the parent, and so on. This setting works nicely with 'set autochdir', because then Vim's current directory is the same as the directory of the file. If you do not like using 'autochdir' but want the same upward search, use:

set tags=./tags;

Here, the leading "./" tells Vim to use the directory of the current file rather than Vim's working directory.

Regardless of the specific search used, you need the +path-extra feature for this tip.

References

:help file-searching, which also gives details about adding "stop directories" to end the upward search

Comments

You can also tag help/man files, and access it from Vim with commands like these in vimrc: